Weierstrass function methodology for uncertainty analysis of random media criticality with spectrum range control

Abstract

Randomized Weierstrass function (RWF) has been under development for evaluating the uncertainty of random media criticality due to the material mixture in disorder. In this work, the modelling capability of RWF is refined so that the spectrum range can be controlled by specifying its lower and upper ends of the frequency domain variable. As a result, it becomes possible to make fair criticality comparison among replicas of random media under inverse power law power spectra. Technically, the infinite sum of trigonometric terms in RWF is formally extended to cover the arbitrarily low frequency domain and then truncated to finite terms for the sole purpose of spectrum range control. This means that the refined RWF is free of the issue of convergence towards a reference fractal characteristic of Weierstrass function and thus termed Incomplete Randomized Weierstrass function (IRWF). As a demonstration, a three-dimensional version of IRWF is applied to the mixture of three fuels with different burnups in a sufficiently water-moderated environment. Monte Carlo criticality calculations are carried out to evaluate the uncertainty of neutron effective multiplication factor (keff) due to the indeterminacy of mixture formation.